The DIS dipole picture cross section in exact kinematics

TL;DR

The paper introduces a finite-energy invariant-mass bound $M^2_{q\bar q} \le W^2$ in the LO DIS dipole picture to capture exact kinematics beyond the optical theorem. By expressing the cross section with both dipole and quadrupole Wilson-line correlators and evaluating the quadrupole with a Gaussian (MV-model) approximation, the authors quantify how the constraint alters $F_L$ and $F_2$ across light and charm quarks. They find modest effects for light quarks (up to ~7% in $F_2$ at $x\sim 0.01$, $Q^2\sim 1\ \mathrm{GeV}^2$) but large suppression for charm (up to ~35% in $F_{2,c}$ and ~8% in $F_{L,c}$) in the same region, with the impact decreasing at smaller $x$ or higher $Q^2$. These results imply finite-energy kinematics are especially important for heavy-quark production and could influence BK initial-condition fits and future DIS analyses at the EIC.

Abstract

We implement a finite energy constraint in the dipole picture of deep inelastic scattering by restricting the invariant mass of the produced partonic system by the virtual photon-target center of mass energy. We show that, for $Q^2=1$GeV$^2$, the effect of this constraint can reach up to $\sim$35% for charm quarks and $\sim$7% for light quarks at $x=0.01$, but then rapidly decreases at smaller $x$ or larger $Q^2$.

Figures (6)

• Figure 1: Diagram representing the $\gamma^* p$ cross-section. The left and right hand sides represent the amplitude and its conjugate, respectively.
• Figure 2: Diagram representing the forward elastic scattering amplitude for $\gamma+p\to\gamma+p$, used to compute the total cross section obtained through the optical theorem.
• Figure 3: Proton structure function $F_L$ (left) and $F_2$ (right) calculated with the finite energy correction, normalized by the optical theorem result. The uncertainty bars indicate the estimated numerical integration uncertainty.
• Figure 4: Phenomenological impact of the finite energy correction on $F_L$ (left) and $F_2$ (right) in the $x$-$Q^2$ plane for light quarks.
• Figure 5: Phenomenological impact of the finite energy correction on $F_L$ (left) and $F_2$ (right) for charm quarks as ratios for selected values of $Q^2$.